A study examined a simple random sample of smokers who tried to quit smoking by using either a nicotine patch or e-cigarettes. Here is a quote from a news article referencing the study: "Quitting is hard. The number of people who quit (within 6 months) was low overall-just 38 of the 584 smokers given the e-cigarette or the patch." Using technology, what is the plus four sample estimate of the proportion of smokers who quit within 6 months using either e-cigarettes or the nicotine patch?

Question

Quizplus · Accepted Answer

To calculate the plus four sample estimate of the proportion, we first need to find the sample proportion (p-hat).

p-hat = 38/584 = 0.0651

Then we add four observations to the sample and add four to the sample size:

New sample size = 588 
New total number of smokers who quit = 38 + 4 = 42

New p-hat = 42/588 = 0.0714

The plus four sample estimate of the proportion of smokers who quit within 6 months is then found by taking the weighted average of the original sample proportion and the new proportion:

(0.0651*584 + 0.0714*4)/(584+4) = 0.0680

Therefore, the answer is C.

A Study Examined a Simple Random Sample of Smokers Who